Solving Equations with xy-yx = 1

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The equation xy - yx = 1 poses challenges for analytical solutions, leading many to suggest numerical methods using software like Mathematica or MATLAB. Historically, this equation has puzzled mathematicians for over 150 years, with recent advancements finally providing clarity. The discussion highlights the difficulty in finding a straightforward analytical method, suggesting that the solutions may be complex. Participants express frustration over the lack of accessible information on the equation's classification. For further details, resources like Wolfram may offer insights into its solutions.
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How can we solve an equation such as xy-yx = 1 without guessing?
 
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I'd solve that equation numerically, using mathematica or matlab.
 
Last edited:
Is there no analytical method? Or is it just horrendously complicated?
 
This question was asked about 150 years ago.
It was only answered recently.
You can find more about its solution somewhere on Wolfram .
 
I can't find anything on it. Does anyone know what the class of equation is called?
 

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